Sunday, October 10, 2010

I've just finished reading a book about ion channels in excitable membranes. Some types of excitable membranes are neurons, hence the interest. The kinetics of these types of cells are really interesting to try to understand. The more complicated or integral parts of sensory processing (and what this means) are performed in such cells.

The different types of channels and subtypes thereof have over time evolved by responding to particular messages or refined their function to respond better to what is happening in the environment. As this blog is not academic, I can voice some gut feelings / hypothesis here without bothering too much about scientific grounding and such. Most of the time, people philosophize over the function of the brain using analogies with existing machineries, comparing it to a computer and so on, but most of the time it becomes really difficult to trace this down towards actual cell function.

I think computer scientists made a bit of a mistake to make sweeping generalizations over the function of a neuron some 60 years ago. The attempt was made to map the function of neurons to something that could run on computer hardware. It started with a model where neurons, because they emitted a potential ( a pulse?! ), could be compared to logic building blocks which either emit a 0 or 1. Just like electronics. The "1" in electronics is basically the 5V of action potential that you'd normally put on a component to communicate a signal.

At some point, the "binary" neuron made way for the sigmoid neuron (so the 'processing kernel' was simply replaced) and this led to networks that were slightly more capable of performing some kind of function. At the moment, a lot of research is undertaken on Spiking Neural Nets (SNN), but there's still not a ground-breaking success in those networks.

I think the reason is that classical nets didn't pose any constraints on the timing of events, because they were mostly used for situations in which each state was information complete and where it was possible to derive the entire output from the combination of inputs (or let's make the output some approximation, as long as it worked, it was fine). Spiking nets do require specific timing constraints and there's not enough knowledge yet to support how such neurons should function over the domain of the signal and time to respond appropriately.

The refinement of using a sigmoid kernel (or tanh kernel) over a binary one is an important one already. The binary kernel was so abrupt in the change, that it was only useful in very specific situations. The sigmoid kernels are more useful, because you can generate proper outputs over a larger dynamic range. But the use of a replaced kernel hasn't been fully exploited yet.

The ion channels of membranes come in roughly three types:- excitatory (generating the potential)- regulatory / rectifying (attempting to establish equilibrium)- modulatory, or acting over a longer time period, having an effect on the excitability of the cell

Classical nets are generally built with some assumed kernel in place and all kernels having the same configuration or parameters. The modulatory effects are not modeled in any way and the calibrati0n of the network is highly focused on the calculation of the weights, assumed to be the efficiency in transfer of neurotransmitters in the synapse.

The book I am reading demonstrates that the fast excitatory and regulatory actions themselves can be modulated somehow (this is like saying that the sigmoid function changes its shape), but that over time or multiple "calculations", this shape can also be modified on the basis of the output of this shape in previous steps (so the output of the kernel is changed as a function of the output of the same kernel in previous steps through some kind of accumulation function).

The classical nets seem very useful to have some alternative, mathematical model using neural networks for very complicated problems, but their abilities may be enhanceable by looking at biologic models in more detail. Neurons do not always function the same way, but you need to look at their behavior over time to see the longer-term effects of repetitive firing, the way how other inputs may influence their behavior (neurotransmitters) and either increase excitability or decrease it (or even suspend it).

However, I am convinced that networks that need to perform real-time tasks, or otherwise tasks where time is explicitly a concern can only be built with networks where this type of modulation and excitation is explicitly built in. The classical nets were never built from this perspective, but they remain interesting for classification or historical data analysis. The controllers (robotics?) of tomorrow and so on should attempt to understand more the dynamics and kinetics of the ion channels in neurons and the ability of neurons to time things.